I've written at some length on this — my ultimate conclusion is that he was not that important for the creation of the atomic bomb. His science was only peripheral to it at most; his letter to FDR was not as important to the timeline as it is often represented; and he himself of course did not work on the Manhattan Project at all. You can see the full post for the details of the argument — obviously it is counterfactual, but as a counterfactual it works to focus our attention on what actually did lead directly to the atomic bomb, and where Einstein's work does or doesn't fit into that. Ultimately his role is frequently exaggerated, and has been since 1945 (including by the officials on the project), because it seems to give the entire project an air of legitimacy, which is interesting to note.